d.o.f = (4-1)*(2-1) = 3*1 = 3
Total x2 = 24.86 > 11.34
Larger that the critical x2 0.01 value .. we reject the null hypothesis
uphill
unbanded
Many banded
total
Site 1
7
Ex= 2.79
X2 = 6.3527
6
Ex=10.21
X2= 1.7350
13
Site 2
7
Ex= 7.29
X2= 0.0115
27
Ex= 26.71
X2= 0.0031
34
Site 3
1
Ex= 6.86
X2= 5.0058
31
Ex= 25.14
X2= 1.3659
32
Site 4
6
Ex= 4.07
X2=0.9152
13
Ex= 14.93
X2= 0.2495
19
total
21
77
98
d.o.f = (4-1)*(2-1) = 3*1 = 3
Total x2 =15.64 > 11.34
Larger that the critical x2 0.01 value .. we reject the null hypothesis
downhill
yellow
Pink &brown
total
Site 1
34 Ex= 36.76 X2= 0.2072
27 Ex=24.24 X2= 0.3143
61
Site 2
14 Ex= 18.08 X2= 0.9207
16 Ex=11.92 X2=1.3965
30
Site 3
24 Ex= 21.69 X2= 0.2460
12 Ex=14.30 X2 = 0.3699
36
Site 4
22 Ex= 17.47 X2= 1.1746
7 Ex=11.53 X2= 1.7798
29
total
94
62
156
d.o.f = (4-1)*(2-1) = 3*1 = 3
Total x2 = 6.409 < 11.34
smaller that the critical x2 0.01 value .. we accept the null hypothesis
downhil
unbanded
Many banded
total
Site 1
4 Ex= 8.21 X2 = 2.1588
57 Ex=52.79 X2= 0.3357
61
Site 2
2 Ex= 4.04 X2= 1.0300
28 Ex= 25.96 X2= 0.1603
30
Site 3
11 Ex= 4.85 X2= 7.7985
25 Ex= 31.15 X2= 1.2142
36
Site 4
4 Ex= 3.90 X2=0.0026
25 Ex= 25.10 X2= 0.0004
29
total
21
135
156
d.o.f = (4-1)*(2-1) = 3*1 = 3
Total x2 = 12.70 > 11.34
larger that the critical x2 0.01 value .. we therefore reject the null hypothesis
We collected our results from 4 different sites of high and low altitudes and noted the snails records according to their shell colour (yellow, pink and brown) and banding pattern (unbanded and many banded). The majority of the snails that was collected were dead .using the chi squared test to investigate the figures, there was no significant difference between the colour and band of C.nemoralis located at high or low altitudes as we have failed to reject the null hypothesis.
the main purpose of chi squared test is to demonstrate if the differences in allele frequency were due to genetic drift or selection and estimates whether the difference in phenotype frequencies is statistically substantial
"Due to the design of this study it is clear that while results do display significance, further development is possible. Whilst a significant amount of data was collected for site comparison, more data would ensure more accurate and reliable readings and would provide a better representative for the entire population. This is not due to any manipulation of data; merely the snails found at each site. It is also worth noting here that live organisms were found in the downhill sites is a key factor to consider here; it is possible that snails in the lower areas (especially brown ones) are more able to survive due to the fact that they may be able to absorb heat more rapidly and hence more able to survive and reproduce. This is a clear example of how selection may be a key factor in explaining why no live snails were found uphill. Additionally many of the snails found uphill were situated next to large trees and vegetation, potentially sheltering them from predators such as birds but more significantly not allowing light to warm them, again meaning they are less likely to survive and reporduce, and increase their numbers in these sights. This again may explain why no organisms were found in the upper sights. The environmental aspect on where live snails were found cannot be ignored. Of course however it is impossible to tell if the snails found live are due to the environmental factors or simply the natural life cycle.
Ultimately, the results indicate a statistical significance between the two chosen sites in terms of the observed phenotypes collected after a chi-square analysis. Results showed that within the uphill samples, there was found to be a greater expected value for unbanded snails found than those that were observed, and similarly the unbanded snails that were observed in the downhill samples found the expected value to be greater further. However, the results indicate that pink unbanded snails were found in greater abundance in the uphill sample, going against the general findings of the other coloured phenotypes, and in contrast, unbanded pink snails were not as prominent in the downhill sample. In this essence, taking account of the coloured phenotype, yellow unbanded snails were found to have no statistical difference between the two regions, however yellow snail observations in general were found more prominently downhill.
Statisical analysis using a Chi-square test comparing the samples of unbanded snails compared to banded snails were found to be significant, thus indicating a difference between the two sites, finding totals larger than the 0.01 X2 critical value. We can therefore reject the null hypothesis. Similarly, tests were conducted on the coloured phenotypes of the samples in both uphill and downhill regions, concluding results also larger than that of the critical value.
Ex= 4.88
X2= 0.0029
Ex=8.12
X2= 0.0018
Ex= 12.75
X2= 2.5931
Ex=21.25
X2=1.5559
Ex= 13.88
X2= 8.9088
Ex=23.12
X2 = 5.3484
Ex= 7.5
X2= 4.0333
Ex=12.5
X2= 2.42
Total x2 = 24.86 > 11.34
Larger that the critical x2 0.01 value .. we reject the null hypothesis
Ex= 2.79
X2 = 6.3527
Ex=10.21
X2= 1.7350
Ex= 7.29
X2= 0.0115
Ex= 26.71
X2= 0.0031
Ex= 6.86
X2= 5.0058
Ex= 25.14
X2= 1.3659
Ex= 4.07
X2=0.9152
Ex= 14.93
X2= 0.2495
Total x2 =15.64 > 11.34
Larger that the critical x2 0.01 value .. we reject the null hypothesis
Ex= 36.76
X2= 0.2072
Ex=24.24
X2= 0.3143
Ex= 18.08
X2= 0.9207
Ex=11.92
X2=1.3965
Ex= 21.69
X2= 0.2460
Ex=14.30
X2 = 0.3699
Ex= 17.47
X2= 1.1746
Ex=11.53
X2= 1.7798
Total x2 = 6.409 < 11.34
smaller that the critical x2 0.01 value .. we accept the null hypothesis
Ex= 8.21
X2 = 2.1588
Ex=52.79
X2= 0.3357
Ex= 4.04
X2= 1.0300
Ex= 25.96
X2= 0.1603
Ex= 4.85
X2= 7.7985
Ex= 31.15
X2= 1.2142
Ex= 3.90
X2=0.0026
Ex= 25.10
X2= 0.0004
Total x2 = 12.70 > 11.34
larger that the critical x2 0.01 value .. we therefore reject the null hypothesis
We collected our results from 4 different sites of high and low altitudes and noted the snails records according to their shell colour (yellow, pink and brown) and banding pattern (unbanded and many banded). The majority of the snails that was collected were dead .using the chi squared test to investigate the figures, there was no significant difference between the colour and band of C.nemoralis located at high or low altitudes as we have failed to reject the null hypothesis.
the main purpose of chi squared test is to demonstrate if the differences in allele frequency were due to genetic drift or selection and estimates whether the difference in phenotype frequencies is statistically substantial
"Due to the design of this study it is clear that while results do display significance, further development is possible. Whilst a significant amount of data was collected for site comparison, more data would ensure more accurate and reliable readings and would provide a better representative for the entire population. This is not due to any manipulation of data; merely the snails found at each site. It is also worth noting here that live organisms were found in the downhill sites is a key factor to consider here; it is possible that snails in the lower areas (especially brown ones) are more able to survive due to the fact that they may be able to absorb heat more rapidly and hence more able to survive and reproduce. This is a clear example of how selection may be a key factor in explaining why no live snails were found uphill. Additionally many of the snails found uphill were situated next to large trees and vegetation, potentially sheltering them from predators such as birds but more significantly not allowing light to warm them, again meaning they are less likely to survive and reporduce, and increase their numbers in these sights. This again may explain why no organisms were found in the upper sights. The environmental aspect on where live snails were found cannot be ignored. Of course however it is impossible to tell if the snails found live are due to the environmental factors or simply the natural life cycle.
Ultimately, the results indicate a statistical significance between the two chosen sites in terms of the observed phenotypes collected after a chi-square analysis. Results showed that within the uphill samples, there was found to be a greater expected value for unbanded snails found than those that were observed, and similarly the unbanded snails that were observed in the downhill samples found the expected value to be greater further. However, the results indicate that pink unbanded snails were found in greater abundance in the uphill sample, going against the general findings of the other coloured phenotypes, and in contrast, unbanded pink snails were not as prominent in the downhill sample. In this essence, taking account of the coloured phenotype, yellow unbanded snails were found to have no statistical difference between the two regions, however yellow snail observations in general were found more prominently downhill.
Statisical analysis using a Chi-square test comparing the samples of unbanded snails compared to banded snails were found to be significant, thus indicating a difference between the two sites, finding totals larger than the 0.01 X2 critical value. We can therefore reject the null hypothesis. Similarly, tests were conducted on the coloured phenotypes of the samples in both uphill and downhill regions, concluding results also larger than that of the critical value.